Graph the system of linear inequalities: -x+y>=3,x+y<=-2,x>=0,y>=0!!! Please help ASAP!!! :(
-x+y>=3 ----> y ≥ x + 3
draw a solid line of y = x+3, shade in the region above it
x+y<=-2 ---> y ≤ -x - 2
draw a solid line of y = -x - 2, shade in the region below it.
x ≥ 0 : shade in the region to the right of the y-axis
y ≥ 0 : shade in the region above the x-axis.
Here are your boundary lines. You do the shading.
What do you think?
forgot the graph:
https://www.wolframalpha.com/input/?i=Plot+-x%2By%3D3,+x%2By%3D-2,+x%3D0,y%3D0
To graph the system of linear inequalities, we will start by graphing each inequality separately, and then find the common region that satisfies all of the inequalities.
1. Begin with the inequality -x + y ≥ 3:
- Replace the inequality symbol with an equal sign to graph the corresponding boundary line: -x + y = 3.
- Solve for y to rewrite the equation in slope-intercept form: y = x + 3.
- Plot the y-intercept, which is (0, 3), and use the slope 1 (since the coefficient of x is 1) to find another point. For example, move one unit to the right from the y-intercept to get the point (1, 4).
- Draw a dashed or solid line passing through these two points.
2. Move on to the inequality x + y ≤ -2:
- Replace the inequality symbol with an equal sign to graph the corresponding boundary line: x + y = -2.
- Solve for y to rewrite the equation in slope-intercept form: y = -x - 2.
- Plot the y-intercept, which is (0, -2), and use the slope -1 (since the coefficient of x is -1) to find another point. For example, move one unit to the right from the y-intercept to get the point (1, -3).
- Draw a dashed or solid line passing through these two points.
3. Consider the inequalities x ≥ 0 and y ≥ 0:
- These inequalities represent the x and y coordinates being greater than or equal to zero, which means they represent the positive quadrants of the graph.
- Draw the x-axis and y-axis on the graph, and shade the region above and to the right of the y-axis.
Finally, identify the common shaded region where all the inequalities overlap. This region represents the solution to the system of linear inequalities.
Please note that without a visual representation, it's challenging to provide an exact graph, but following these steps should help you plot the system accurately.